Write the equation of a line that is parallel to ${y=-\dfrac{5}{4}x+7}$ and that passes through the point ${(-4,1)}$.
Solution: Getting started Key idea: Parallel lines have the same slope. Step 1: Find the slope Slope of the given line: ${-\dfrac{5}{4}}$ Slope of the parallel line: $C{-\dfrac{5}{4}}$ Step 2: Substitute the known point into linear equation The parallel line will have a slope of $C{-\dfrac{5}{4}}$ and pass through the point ${(-4,1)}$. Let's start from the point-slope form of the equation of the parallel line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{1} &= C{-\dfrac{5}{4}}(x-{(-4)})\\\\\\ y-1 &= C{-\dfrac{5}{4}}x -5 \\\\\\ y &= C{-\dfrac{5}{4}}x {-4} \end{aligned}$ Answer The equation of the parallel line is $y = C{-\dfrac{5}{4}}x {-4}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$